OFFSET
4,7
COMMENTS
When the board is rotated 180 degrees, the diagram remains the same, but the tour reverses direction.
REFERENCES
D. E. Knuth, Long and skinny knight's tours, in Selected Papers on Fun and Games, to appear, 2010.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 4..4057
George Jelliss, Open knight's tours of three-rank boards, Knight's Tour Notes, note 3a (21 October 2000).
George Jelliss, Closed knight's tours of three-rank boards, Knight's Tour Notes, note 3b (21 October 2000).
FORMULA
a(n) = 0 unless n mod 2 = 0.
Generating function: (2*(2*z^10 - 8*z^14 + 24*z^16 - 76*z^18 + 32*z^20 + 288*z^22 - 716*z^24 + 792*z^26 - 336*z^28 - 2908*z^30 + 7896*z^32 - 1464*z^34 - 3432*z^36 + 7416*z^38 - 32616*z^40 - 11792*z^42 + 39888*z^44 + 35472*z^46 + 47968*z^48 + 35776*z^50 - 143424*z^52 - 197824*z^54 - 15552*z^56 - 11008*z^58 + 181376*z^60 + 269440*z^62 + 78080*z^64 + 53760*z^66 + 44288*z^68 - 48128*z^70 - 112640*z^72 - 124928*z^74 - 227328*z^76 - 155648*z^78 + 98304*z^80 + 147456*z^82 + 32768*z^84))/
(1 - 6*z^4 - 64*z^8 + 200*z^12 + 1000*z^16 - 3016*z^20 - 3488*z^24 + 24256*z^28 - 23776*z^32 - 104168*z^36 + 203408*z^40 + 184704*z^44 - 443392*z^48 - 14336*z^52 + 151296*z^56 - 145920*z^60 + 263424*z^64 - 317440*z^68 - 36864*z^72 + 966656*z^76 - 573440*z^80 - 131072*z^84)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 10 2010, based on a communication from Don Knuth, Apr 28 2010
EXTENSIONS
More terms extracted from the g.f. by R. J. Mathar, Oct 09 2010
STATUS
approved